(1) Technical Field
The present invention is related to a device and method for three-dimensional (3-D) imaging and, more specifically, to a single-lens 3-D imaging device using a polarization-coded aperture mask combined with a polarization-sensitive sensor.
(2) Background
Three-dimensional (3-D) imaging is a continuously evolving field that would benefit from improved imaging techniques. Enhanced 3-D imaging could be used for a variety of purposes, such as to generate quantitative information about an imaged object (through quantitative 3-D imaging). However, existing imaging techniques have failed to sufficiently support quantitative 3-D imagining. For example, when a point that is not on the focal plane of an imaging system is imaged through the imaging system, the captured point detected by a sensor is said to be defocused. If the imaging system has a large aperture, then the defocused point will appear blurred. For this reason, it has been suggested that the blur of the image of a point can be used to quantitatively determine the distance from that point to the focal plane in space. It has also been suggested that if the position of the focal plane is known, the imaging system could be used for quantitative 3-D imaging. To reconstruct the 3-D position of a point, it is only necessary to measure the size and/or intensity of the blur disc (Z) and the point position on the sensor (X, Y).
In practice, however, such a system is difficult to effectively implement. First, a blurred image occupies a large amount of space on the sensor, so sophisticated algorithms to separate overlapped images are necessary. Second, the amount of light entering the optical system does not change appreciably between a focused point and a defocused point (unless the focal plane is very close to the optical system). Thus, the blurred image puts the same amount of energy onto the sensor as a focused image, but spread over a larger area. The intensity of a defocused image is inversely proportional to its area, so a quantitative measurement of the distance between the focal plane and a point based only on blur requires a sensor with an extremely high dynamic range. In real lenses, there are also diffraction effects which make blurred images look more like rings than broad Gaussian distributions in certain depth ranges, making software processing complicated. See, for example, Wu, M.; Roberts, J. W.; and Buckley, M., “Three-dimensional fluorescent particle tracking at micron-scale using a single camera,” Experiments in Fluids, 2005, 38, 461-465. Even without lens aberrations or diffraction, image processing is complicated by the fact that since the depth information comes from a measure of the diameter of a blur spot, the intensity of the imaged point affects the measurement. For example, if two defocused points A and B have the same amount of defocus, but point A is brighter than point B, typically point B's image will be measured as having a smaller diameter than point A's simply because it does not rise as far from the background illumination in the scene.
The original “defocusing” concept recognized that in such a blur-based system, the depth information is carried only by the marginal (outer) rays of the ray pencil that forms the image. See, for example, Willert, C. E.; and Gharib, M., “Three-dimensional particle imaging with a single camera,” Experiments in Fluids, 1992, 12, 353-358. It is the angle that these rays make with the sensor plane that dictates the sensitivity of the imaging system. Thus, an equivalent measurement should be possible by placing small apertures off-axis in the imaging system, such that only marginal rays may pass through to form an image. If a blur system, as described above, has its large aperture replaced with a small aperture placed anywhere on the circumference of the large aperture, then the image of a defocused point is now a small spot located on what would otherwise be the circumference of a blurred image. The end result is depth information that is transmitted not by the size of a blurred spot, but rather by a lateral offset in a much smaller spot. Measuring the location of a spot on an image is much less sensitive to intensity differences than measuring its size.
The use of small apertures alleviates the dynamic range issues with a blur-based system, since the high f-number of the small aperture makes diffraction blur (not defocus blur) the primary blurring agent in the image. This means that within a large range of distances from the focal plane, the images are almost the same size.
Using off-axis apertures means that reconstruction of a point's position in space now involves finding all the images of a single point on the sensor and measuring the distance between them. The images will appear in the same pattern as the aperture arrangement; for example, if three small apertures arranged as vertices of an equilateral triangle are used, then the image of a defocused point is three small spots arranged in an equilateral triangle. The orientation of the images' triangle relative to the apertures' triangle reveals whether the defocused point is ahead of or in front of the focal plane. Additionally, the size of the images' triangle relates to the distance between the defocused point and the focal plane. The size of the triangle is zero for a focused point which occurs when all three images are on top of each other. The size of the triangle increases as the amount of defocus increases. Multiple small images take up less space on the sensor than one large blurred one, so the overlap problem is alleviated by this arrangement.
The matching problem in the reconstruction creates a new problem; if the object being imaged is a set of featureless points, then the images are indistinguishable and can only be matched according to their relative location (for example, finding all dots on an image that form equilateral triangles within some tolerance). This relatively loose matching criterion necessitates that three or more apertures be used to reduce the number of mismatches or “ghosts.”
A single off-axis aperture records depth information; however, Z cannot be separated from the in-plane position of the point imaged. Two apertures record the depth information and allow the in-plane position to be extracted independently of Z. In practice, it is impossible to reconstruct a random point cloud with only two apertures because many ghost particles are generated when images are mismatched. Moreover, it is impossible to know if a particle was in front of or behind the focal plane from only two images. With three apertures, mismatches are reduced and the sign of the distance from the particle to the focal plane is known by the orientation of the triangle formed by the images.
See, for example, Willert, C. E.; and Gharib, M., “Three-dimensional particle imaging with a single camera,” Experiments in Fluids, 1992, 12, 353-358.
The original practical implementation of the defocusing concept consists of a single lens with three off-axis apertures imaging onto a single monochromatic sensor (i.e., three was deemed the minimum number of apertures that produced acceptable results). It should be noted that because the defocusing measurement is a measurement of a point's position relative to the focal plane, it is necessary to know the position of the device to know the absolute position of desired point.
The three off-axis apertures imaging onto a single monochromatic sensor also has disadvantages. Overcrowding of the sensor is still an issue when the point density within the scene is high. In this case, each point has up to three images on the sensor and there is still a possible dynamic range issue (i.e., a point on the focal plane will have three images that coincide on the sensor and thus will look three times as bright as defocused points). The dynamic range issue can be overcome by selectively illuminating the volume so that no points on the focal plane are imaged.
As described in U.S. Pat. Nos. 6,955,656 and 7,006,132, one solution to the overcrowding problem is to image each aperture with a separate sensor. This adds to the matching criterion, because now each spot on the image can only be one of the vertices of the aperture arrangement; since the source (aperture) of each spot is known, there is slightly less ambiguity in the matching process.
Further, the addition of more sensors (for example, a charge-coupled device (CCD)) has the disadvantages of higher cost and larger size (along with manufacturing complications) relative to a single-sensor system. Moreover, multiple-sensor arrangements pose alignment challenges and robustness challenges; the multiple sensors are also differently affected by temperature, vibration, and other environmental effects and as such are more prone to calibration errors.
For the foregoing reasons, there is a need for a quantitative 3-D imaging system which either alleviates or eliminates the matching problem. The system should be viable in a single-lens, single-sensor arrangement for simplicity and compactness and also should be easily expandable to a multiple-lens, multiple-sensor arrangement if so desired.